The Deligne--Milnor formula

Abstract: Let $X \to S$ be a family of algebraic varieties parametrized by an infinitesimal disk $S$, possibly of mixed characteristic. Bloch's conductor conjecture expresses the difference of the Euler characteristics of the special and generic fibers in algebraic and arithmetic terms. I'll describe a proof of some new cases of this conjecture, including the case of isolated singularities. The latter was a conjecture of Deligne generalizing Milnor's formula on vanishing cycles. (This is based on joint work with Massimo Pippi.)

number theory

Audience: researchers in the topic

London number theory seminar

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